AnswerBun.com

General solution of an ODE from the general solution of a PDE/SDE/SPDE and most general "differential" equation

Is it possible to obtain the general solution of an ODE by solving a PDE, SDE or SPDE? I haven’t dived into PDEs, nor SDEs, therefore the question.

Another question that arises from my love to differential equations and love for general cases. From a higher mathematical perspective, how PDEs and SPDEs can be generalized? I was thinking of a more general operator that behaves like the differential operator in certrain structures, instead of use real numbers use hypercomplex numbers (from the Cayley–Dickson construction or Clifford algebras) or things a lot more general that I don’t know. Instead of limiting to apply the operator once, twice or thrice extend it in a way that it is possible to apply a hypercomplex number of times (if the Gamma function were involved, for example, there’s a way to extend it to hypercomplex numbers from the Cayley–Dickson construction, via defining the Gamma function of a matrix). Hence, what is the most general kind of differential equation that you know? and, what is the most general kind of (not necessarily differential) operator that you know?

Mathematics Asked by Andrés M. Santos Ramírez on December 30, 2020

0 Answers

Add your own answers!

Related Questions

Most General Unifier computation

1  Asked on February 16, 2021 by milano

   

$sigma(n)$ is injective?

1  Asked on February 14, 2021 by ferphi

   

Find area of equilateral $Delta ABC $

2  Asked on February 14, 2021 by ellen-ellen

     

Diagonal of parallelogram and parallelepiped

0  Asked on February 13, 2021 by return

 

Ask a Question

Get help from others!

© 2022 AnswerBun.com. All rights reserved.